Fluid flows and particle flows of at least partially electrically charged particles can be realized by the application of electric fields. In this connection, electroosmosis and electrophoresis, which are classified as electrokinetic effects, are the important physical phenomena that occur.
Electroosmosis is described as the motion of a fluid under the influence of an externally induced electric field. At the surface (wall) of a substrate, electric charges are typically present. If the surface comes in contact with a fluid containing mobile electric charges, what is commonly known as an electrical double layer forms. The charge at the surface of the substrate attracts charge carriers of the fluid whose charge is opposite that of the surface charge. Because of the excess of charge, the electroneutrality of the fluid is then no longer given in the electrical double layer. The externally induced electric field causes the excess charge carriers in the electrical double layer to migrate in a preferential direction. The ensuing viscous interactions thereby induce a motion in the surrounding fluid. The velocity of the motion is proportional to the magnitude of the electric field. The proportionality factor is referred to as electroosmotic mobility.
Electrophoresis is understood to be the directed movement of at least partially electrically charged particles in a fluid or a gel under the action of an external electric field. The velocity of the particles is proportional to the magnitude of the electric field. The proportionality factor is referred to as electrophoretic mobility. Typically, the mobilities are specific and dependent on the surrounding fluid.
To drive a fluid flow by electroosmosis, an electric DC-voltage field is used that is generated by introducing an electrode pair into the fluid. The electric field component, which is tangential to the wall of a substrate, induces the flow in the region of the electrical double layer. Flow velocities in the mm/s range are typically attainable when electric fields on the order of kV/cm are used. The electroosmotic mobility depends, in particular, on the wall charge and the concentration of the mobile charge carriers in the fluid.
In response to a rise in the concentration of the mobile charge carriers, the number of particles upon which the electric field forces act increases, thereby inducing the flow. At the same time, however, the thickness of the electrical double layer decreases, thereby reducing the volume within which the forces act. These opposite effects yield an optimum charge concentration.
Due to the electroosmosis, it is possible for a flow to be produced without the use of mechanical components. Therefore, the principle is especially applicable to geometries having microscale dimensions. In a straight microchannel, a virtually uniform (plug-shaped) velocity profile is obtained over the width of the channel. This is especially beneficial for the transport of biological cells and other particles which must not be subject to the action of substantial shear forces.
Electrophoresis is used as a separation process for mixtures of at least partially electrically charged particles. To that end, the particles are typically injected into a microfluidic channel geometry having small dimensions, such as a capillary tube. The geometry is filled with a fluid which is used as a sample carrier. Similarly to the case of electroosmosis, an electrode pair is introduced into the geometry, and a DC-voltage field is produced. The particles move within the electric field in their specific direction of motion and at their specific velocity. If there is an appreciable difference in the electrophoretic mobility of the particle types, then a separation resolution of the particles by type is achieved. Migration velocities in the mm/s range are typically attainable when electric fields on the order of kV/cm are used.
In the context of both electrokinetic effects, an electrode pair is introduced into a fluid. For technical applications, the electric voltages are in the kV range. Since, typically, the fluids used are mostly composed of water, the high voltages induce electrolysis reactions, whereby the water breaks down into hydrogen and oxygen. These outgas therefore, induce undesired secondary flows and interfere with the local conductivity. Typical values of the equilibrium potentials of the decomposition reactions under standard conditions (activity 1 mole/dm3, T=298 K) are on the order of 1 V. However, the equilibrium potential represents only the value required for the thermodynamic course of the reaction. In practice, due to reaction inhibitions, the value of the potential is appreciably higher than the equilibrium potential.
The high voltages used produce a relatively high electric current in the fluid, whereby the Joulean heat causes the fluid to be heated. The rise in temperature has a negative effect, especially in the case of analytical procedures. Natural convection and an inhomogeneous temperature profile degrade the separation efficiency and resolution. Therefore, the use of high voltages is frequently ruled out, and electroosmosis and electrophoresis are restricted in their technical use.
In Model and Verification of Electrokinetic Flow and Transport in a Micro Electrophoresis Device, Lab on a Chip 2005, volume 5, pp. 949-958, D. P. J. Barz and P. Ehrhard describe the theory of electroosmosis and electrophoresis. For straight and slightly curved geometries, the electroosmotic velocity uEO at the transition of the electrical double layer to the electrically neutral turbulent core, thus at a small distance to the wall, is expressed asuEO=(qzeta·lD/η)Et,
Et being the external electric field component that is tangential to the wall. Prefactor qzeta·lD/η represents a formulation of the electroosmotic mobility, which is made up of the electric charge density qzeta at the shear plane between the adsorbed and diffuse charge layer, of the thickness ID of the electrical double layer, and of dynamic viscosity η of the fluid. Given knowledge of zeta potential ζ, the charge density at the shear plane may be determined fromqzeta=−εξ/lD,
ε being the permittivity of the fluid. The electrophoretic velocity uEP of an electrically charged particle under the influence of an electric field E is expressed asuEP=λEPE.
The electrophoretic mobility λEP of the particle can be calculated in the context of simple ions in infinite dilution, otherwise it can be determined by measurement.
In Effect of Joule Heating on Efficiency and Performance for Microchip-Based and Capillary-Based Electrophoretic Separations: A Closer Look, Electrophoresis 2004, volume 25, pp. 253-269, N. J. Petersen, R. P. H. Nikolajsen, K. B. Mogensen and J. P. Kutter illuminate how a temperature increase caused by Joulean heat influences electrophoretic separation systems. It is ascertained that the temperature of the fluid rises proportionally to the square of the electric field strength. In conventional capillaries, a boiling of the fluid can be observed already at relatively low electric field strengths. Such effects are not observed in planar microfluidic units given comparable conditions. Theoretical calculations reveal, however, that, in the case of capillaries and planar units, at or above a specific electric field strength, a radial temperature profile develops, and the separation efficiency is thereby degraded.
In Zeta Potential of Microfluidic Substrates: 2. Data for Polymers, Electrophoresis 2004, volume 25, pp. 203-213, and in Zeta Potential of Microfluidic Substrates: 2. Data for Polymers, Electrophoresis 2004, volume 25, pp. 203-213, B. J. Kirby and E. F. Hasselbrink Jr. describe the correlation between the Zeta potential and systems frequently used in microfluidics, thus the pairing of the fluid and substrate of the microfluidic unit. The zeta potential for glass, silicates and many plastics is predominantly negative over a broad variation range of the pH value and the fluid. However, plastics also exist, such as polyamides at pH≦6, that exhibit a positive zeta potential.
In Field-Effect Flow Control for Microfabricated Fluidic Networks, Science 1999, volume 286, pp. 942-945, R. B. M. Schasfort, S. Schlautmanm, J. Hendrickse and A. van den Berg describe a method for manipulating the zeta potential at the walls of microchannels which are fabricated from a semiconductor material, and discuss the results of such experiments. To this end, they introduce two electrodes into a microchannel that is filled with a fluid. The voltage between the electrodes induces an electroosmotic flow. An additional electric field is then induced between a third electrode outside of the channel wall and the fluid, perpendicularly to the channel wall. The zeta potential and, thus, the electroosmotic flow are influenced by the potential at the third electrode. It is described how, in response to the third electrode changing from a positive potential to a negative value, the flow direction and, therefore, the plus/minus sign of the zeta potential also change.
In Patterning Electro-osmotic Flow with Patterned Surface Charge, Physical Review Letters 2000, volume 84, pp. 3314-3317, A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov and G. M. Whitesides describe the behavior of the electroosmotic flow in a channel having different surface charges. To that end, two opposite walls of a rectangular channel are provided with two different coatings. Following the coating process, both walls have a similar charge density amount, but differ in their sign. If an electric field is then applied along the channel wall, a linear flow profile results. Starting from a positive velocity u at the negatively charged wall, the velocity falls to zero when approaching the middle of the channel, to finally reach value −u at the positive wall. In another configuration, one channel wall is coated in a such a way that a regularly alternating structure of positive and negative surface charges results. In response to the application of an electric field in the direction of the channel, vortices form over the treated sections. The direction of rotation of the vortices is dependent on the sign of the surface charge. When such an arrangement is used, it is not possible for a fluid transport of any significance to be achieved. Moreover, such an arrangement cannot be used for analytical processes.
In Electroosmotic Pumping in Microchips With Nonhomogeneous Distribution of Electrolytes, Electrophoresis 2002, volume 23, pp. 1862-1869, R.-L. Chien and L. Bousse describe coating the interior of a capillary with a polymer in order to reduce the value of the zeta potential and thus the electroosmotic flow velocity.
In Low-Voltage Electroosmosis Pump for Stand-Alone Microfluidics Devices, Electrophoresis 2003, volume 24, pp. 185-192, Y. Takamura, H. Onoda, H. Inokuchi, S. Adachi, A. Oki and Y. Horiike describe a pump based on fluid flows produced by electroosmosis. To increase their efficiency, it is theoretically proposed to connect in series two individual pumps having opposite zeta potential, which, from opposite electric fields, produce the same flow direction. However, the authors reject this approach as being hardly feasible. Rather, they construct a highly efficient pump by connecting in series regions of small and large cross section that are inserted in a meander form between a positive and a negative electrode. It turns out that this configuration has the drawback of a large surface-area requirement and low flexibility.
The European Patent EP 0 727 661 B1 describes a method and a device for mixing fluids, which provide for an electroosmotic pump to transport the two fluids to be mixed to a connection point, where they are mixed. The inherent disadvantages here are the use of capillaries, the high voltage requirement, as well as the lack of flexibility.
In Pumping Based on Transverse Electrokinetic Effects, Applied Physics Letters 2003, volume 83, pp. 1486-1488, I. Gitlin, A. D. Stroock, G. M. Whitesides and A. Ajdari describe a microfluidic pump where a transversal electric field induces a longitudinal flow along the channel direction in a channel into which oblique recesses have been introduced into one wall. This article also discusses controlling such flows by the application of voltages between channel intersections. In this arrangement, the flow is bound to the channels, the rate of net transport is low, and the essentially helical trajectories inevitably subject the fluid flows at the intersections to a mixing process that is not necessarily desirable.
From V. Studer, A. Pépin, Y. Chen and A. Ajdari, An Integrated AC Electrokinetic Pump in a Microfluidic Loop for Fast and Tunable Flow Control, Analyst 2004, volume 129, pp. 944-949, an asymmetrical electrode arrangement on a homogeneous substrate is described, which, by employing an AC voltage in the 1-10 kHz range, functions as a microfluidic pump. Other arrangements of this kind which are operated using AC voltage, are described in the European Patent Specification EP 0 595 290 B1 and the German Patent Application DE 101 03 399 A1. One possible mechanism of the alternating-field electroosmosis resides in the heating of the fluid by the induced electric field. In response to the heating, the permittivity of the fluid changes locally. Electric volumetric forces can thereby be induced in the presence of an inhomogeneous electric field. However, this phenomenon is typically not very pronounced.
In AC Electric Field-Induced Fluid Flow in Microelectrodes, J. Colloid and Surface Sciences 1999, volume 217, pp. 420-422, A. Ramos, H. Morgan, N. G. Green and A. Castellanos describe a different thesis. In the case of alternating-field electroosmosis, not only is the electric field inhomogeneous and dependent on the frequency, but a component of the electric charge density of the electrode surface is coupled to the frequency. At high frequencies, the potential mostly falls off in the electrolyte, the induced charge in the electrical double layer is small, and the resulting flow, therefore, as well. At low frequencies, the potential mostly falls off over the electrical double layer, the tangential component of the electric field is small, and, again, no appreciable flow develops. However, an appreciable laminar flow forms at middle frequencies.
In Pumping of Liquids With Travelling-Wave Electroosmosis, Journal of Applied Physics 2005, volume 97, pp. 084906-1 to 084906-8, A. Ramos, H. Morgan, N. G. Green, A. Gonzales and A. Castellanos describe another arrangement for generating an electroosmotic flow. To that end, an arrangement of a plurality of regularly interspaced, small symmetrical electrodes are attached to the channel wall. A voltage signal in the form of a sinusoidal signal is then induced at the electrode arrangement. The voltage at two successive electrodes exhibits a 90° phase displacement. This arrangement makes it possible for appreciable liquid flows to be produced at amplitudes of 1 volt. However, the prevailing mechanisms are not fully clarified. Thus, for example, above a certain threshold value of the voltage amplitude, the flow direction changes. Moreover, the threshold value appears to be dependent on the electrode material. Furthermore, a relatively high velocity of the fluid tangentially to the main flow direction is apparent in this method, which can be problematic in terms of an analytical use.
European Patent Application EP 1 362 827 A1 describes the principle of producing fluid flows and/or particle flows of at least partially electrically charged particles contained in a fluid, where the force derived from oppositely directed electric fields induces a rectified flow of the fluid tangentially to the surface of the substrate.
A method known from the prior art for utilizing electrokinetic effects for lab-on-a-chip applications is depicted in FIG. 1a and FIG. 1b. Two electrodes are interspaced at a considerable distance in a microstructure. In accordance with FIG. 1a, a high voltage is applied in between the two electrodes to generate an electric field that penetrates a large volume of the microstructure in such a way that a current flow and, thus, Joulean heat is induced everywhere in this region.
Due to the relatively uniform zeta potential along the surface of the substrate in accordance with FIG. 1b, the electric field generates a uniform force field and, therefore, an electroosmotic flow. A mixture of at least partially electrically charged particles within the electrical double layer and externally therefrom resolves into its constituents under the influence of the electric field.
In terms of the application in an electrophoretic separating unit, this is a desired effect. However, the arrangement does not permit the simple transport of mixtures of at least partially electrically charged particles, which, in many cases, has a disadvantageous effect. Moreover, due to the high voltage between the electrodes, there is still the probability of electrolytic decomposition reactions of the fluid.
FIGS. 1a and 1b illustrate the prior art. If two adjacent electrodes 1, 1′ are supplied with a positive and negative DC voltage, respectively, this yields an electric field 2. If a homogeneous surface charge is present at surface 3, a force field 4 forms within the electrical double layer, inducing a flow 5. Positively charged particles migrate in direction 6 of the negatively charged electrode. Negatively charged particles migrate in direction 7 of the positively charged electrode.